Temporal and spatial coherence of sound at 250 Hz and 1659 km in the Pacific Ocean: Demonstrating internal waves and deterministic effects explain observations
Five sections where blind predictions of coherence time have been made. (A) 3115 km between a bottom-mounted source on Kauai (75 Hz, 0.03 s resolution) and a towed receiver, (B) 3683 km between the same source and a towed receiver, (C) 3709 km between a bottom-mounted source at Kaneohe Bay, Oahu (133 Hz, 0.06 s resolution) to SOSUS station mounted on the bottom, (D) 3250 km transmission between source dangled from R/V Flip (75 Hz, 0.03 s resolution) and a vertical array, and (E) 1659.32 km transmission reported in this paper between a source moored over the Hoke seamount (250 Hz, 0.02 s resolution) and a towed array. Heading of the towed array is 12° true (arrow).
Coherent average of impulse response from Hoke source (A) compared with two models [(B) and (C)]. Travel time of the data is adjusted to approximately coincide with the models. Only panels (B) and (C) have amplitudes that can be compared. PE is the parabolic approximation. Panel (B) shows an incoherent average (thick line) from many realizations of the impulse response computed at different geophysical times through an evolving field of internal waves. The thin line shows one of those realizations. Panel (C) is the impulse response computed through a climatological average of sound speed without perturbations from internal waves.
Two estimates of bathymetry along section E in Fig. 1. Both estimates incorporate experimental measurements of bathymetry within 2.8 km of the acoustic source moored over the Hoke seamount (Ref. 11). The thicker line is from a 1987 database of depth (Ref. 19). The thinner is from a 2006 database (Ref. 20).
Time fronts at distances of 100, 800, and 1659 km from source in panels (A), (B), and (C), respectively. Levels shown are in upper 38 dB at each distance. Depths of the water and basement are dashed and solid lines, respectively. Each panel shows 1.5 s of acoustic travel time. Top dashed line in panel (C) is at depth of the receiver. Time fronts are modeled with the parabolic approximation (Ref. 21) for a snapshot of sound-speed fluctuations due to internal waves added to a climatological background.
Probability distribution of coherence time from section E (Fig. 1) for the data (A) and model (B). Data come from a single transmission of the Hoke source covering 1.833 min. Coherence time of the data is discretized to 12.276 s, the period of each of the nine transmitted -sequences. Coherence time of the model is discretized at 12 s intervals. Coherence times from data and model are analyzed on the same basis. Actual coherence times may extend past 1.833 min, but cannot be explored with a transmission of 1.833 min. The sum of the probabilities is one for each panel separately.
Modeled estimates of the normalized horizontal correlation coefficient of the acoustic field for section E in Fig. 1 at 250 Hz with 95% confidence limits shown. The dotted line is at exp(−1). The correlation decreases with separation because of the effects of internal gravity waves.
(A) Contours of top 30 dB of 61 impulse responses, at 3-h intervals, computed from the parabolic approximation model for section E in Fig. 1. Modeled variations are due to the time evolution of a standard internal wave field. (B) Incoherent average of the 61 impulse responses used in (A) [same as thick line in Fig. 2(b) except amplitudes are scaled with a different value].
Summary of five experiments where a Monte-Carlo technique is used to see if modeled and measured coherence times of sound are consistent. Section letter refers to Fig. 1. Analysis of sections A, B, and C are from Refs. 3–5, respectively. Results from section D are inconclusive because observations of coherence time may not quite be complete (Ref. 6). This paper concerns section E.
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